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  <div class="section" id="numpy-random-generator-chisquare">
<h1>numpy.random.Generator.chisquare<a class="headerlink" href="#numpy-random-generator-chisquare" title="Permalink to this headline">¶</a></h1>
<p>method</p>
<dl class="method">
<dt id="numpy.random.Generator.chisquare">
<code class="sig-prename descclassname">Generator.</code><code class="sig-name descname">chisquare</code><span class="sig-paren">(</span><em class="sig-param">df</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.Generator.chisquare" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw samples from a chi-square distribution.</p>
<p>When <em class="xref py py-obj">df</em> independent random variables, each with standard normal
distributions (mean 0, variance 1), are squared and summed, the
resulting distribution is chi-square (see Notes).  This distribution
is often used in hypothesis testing.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>df</strong><span class="classifier">float or array_like of floats</span></dt><dd><p>Number of degrees of freedom, must be &gt; 0.</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  If size is <code class="docutils literal notranslate"><span class="pre">None</span></code> (default),
a single value is returned if <code class="docutils literal notranslate"><span class="pre">df</span></code> is a scalar.  Otherwise,
<code class="docutils literal notranslate"><span class="pre">np.array(df).size</span></code> samples are drawn.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>out</strong><span class="classifier">ndarray or scalar</span></dt><dd><p>Drawn samples from the parameterized chi-square distribution.</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>ValueError</strong></dt><dd><p>When <em class="xref py py-obj">df</em> &lt;= 0 or when an inappropriate <em class="xref py py-obj">size</em> (e.g. <code class="docutils literal notranslate"><span class="pre">size=-1</span></code>)
is given.</p>
</dd>
</dl>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The variable obtained by summing the squares of <em class="xref py py-obj">df</em> independent,
standard normally distributed random variables:</p>
<div class="math">
<p><img src="../../../_images/math/22081b0dd7eea6bb89b5aa8e6c90e24e0f86282a.svg" alt="Q = \sum_{i=0}^{\mathtt{df}} X^2_i"/></p>
</div><p>is chi-square distributed, denoted</p>
<div class="math">
<p><img src="../../../_images/math/4f1e7743007979f7c1e074c8e557ca980338564c.svg" alt="Q \sim \chi^2_k."/></p>
</div><p>The probability density function of the chi-squared distribution is</p>
<div class="math">
<p><img src="../../../_images/math/c34b7f3860284895cc673379632ae9db40e44670.svg" alt="p(x) = \frac{(1/2)^{k/2}}{\Gamma(k/2)}
x^{k/2 - 1} e^{-x/2},"/></p>
</div><p>where <img class="math" src="../../../_images/math/e7003fd3463f843ee1e53385878369f078d362ad.svg" alt="\Gamma"/> is the gamma function,</p>
<div class="math">
<p><img src="../../../_images/math/56038a4f969ede6d5255837ac81ecde1965079e4.svg" alt="\Gamma(x) = \int_0^{-\infty} t^{x - 1} e^{-t} dt."/></p>
</div><p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r32b5162c4983-1"><span class="brackets">1</span></dt>
<dd><p>NIST “Engineering Statistics Handbook”
<a class="reference external" href="https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm">https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">()</span><span class="o">.</span><span class="n">chisquare</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">)</span>
<span class="go">array([ 1.89920014,  9.00867716,  3.13710533,  5.62318272]) # random</span>
</pre></div>
</div>
</dd></dl>

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